The Fine Gael leader, Mr John Bruton, criticised the IRA for not declaring that "the war is over". The meaning of those words was crucial and very simple, he said.
Criticising the statement of the Sinn Fein leader, Mr Gerry Adams, that violence must now be "a thing of the past, over, done with and gone", Mr Bruton said it was "just a statement of a wish", not a statement of what the IRA would actually do in all circumstances.
He also sharply criticised the paramilitary group for not accepting the referendum vote on the Belfast Agreement as an act of national self-determination. "It is criminally wrong for the IRA to deny that, because in denying it they are providing an implicit justification for the `Real IRA'. It is wrong for Sinn Fein to support or condone that continuing Provisional IRA position.
"Why will the IRA not say the war is over? Why is the Irish Government afraid to ask them to say so? Why is the Government afraid of the answer it will get?"
Mr Bruton said the Government had declined to call on the IRA to make a clear statement. "Indeed, it engaged in surprisingly similar evasion to that of the IRA itself."
But Sinn Fein's representative in the Dail, Mr Caoimhghin O Caolain (Cavan-Monaghan), hit out at the Fine Gael leader and said he was "out of step" with everyone else and was still "failing to grasp the reality" of the peace process or "show an acceptance" of the day-to-day reality of implementing the peace process.
During a series of statements on the Omagh bombing, Mr Bruton said that "as long as the IRA's own war cannot be said to be over, the republican movement is saying that there are still some unstated circumstances in which violence might actually be `defensible'.
"That continuing ambiguity provides a moral cover for the `Real IRA' and for its activities at Omagh."
Some "well-intentioned people" liked to believe that Sinn Fein and the IRA were two separate organisations and that the Sinn Fein peace strategy could be assessed separately from that of the IRA.
"That is nonsense. At the top level, the direction of the two organisations is identical in philosophy, purpose and execution. They are one and the same. Two organisations in one movement, with one purpose, one strategy and one direction."
If the IRA said the Belfast Agreement referendum "was not a valid exercise in national self-determination, then that is what the Sinn Fein leadership believes too".
He added that "violence committed by republicans for political ends, after that 1998 referendum result, is of an entirely different character to violence committed beforehand, in terms of republican ideology".
Mr Bruton believed that the IRA statement of April 30th was part of a "carefully-nuanced republican strategy to allow the luxury of an each-way bet on the Good Friday Agreement". This "has created the political space in which the `Real IRA' can claim a spurious sense of republican justification for bombing campaigns".
He said there was a "continuing contradiction between the recent public statements of the Provisional IRA and the logic of the peace process initiated by Gerry Adams and John Hume. It is a contradiction which allows a political space for the Omagh bombers. Until that contradiction is resolved, we will not have lasting peace."
Mr O Caolain said that "now is not the time for party-politicking or point-scoring, for recriminations or the placing of new obstacles to progress. "The bombing of Omagh was an attack on the peace process in general and on the Sinn Fein peace strategy in particular. It ran completely contrary to the democratic consensus among Irish republicans.
"Those who carried out the bombing hold themselves accountable to no community or political constituency. I believe that the republican consensus, and the weight of public opinion generally, will ensure that their ill-conceived campaign, unbearably tragic though its consequences were in Omagh, will have been short-lived," he said.